Empirical mode decomposition of multiphase flows in porous media: Characteristic scales and speed of convergence

Abstract

We apply a proper orthogonal decomposition (POD) to data stemming from numerical simulations of a fingering instability in a multiphase flow passing through obstacles in a porous medium, to study water injection processes in the production of hydrocarbon reservoirs. We show that the time evolution of a properly defined flow correlation length can be used to identify the onset of the fingering instability. Computation of characteristic lengths for each of the modes resulting from the POD provides further information on the dynamics of the system. Finally, using numerical simulations with different viscosity ratios, we show that the convergence of the POD depends non-trivially on whether the fingering instability develops or not. This result has implications on proposed methods to decrease the dimensionality of the problem by deriving reduced dynamical systems after truncating the system’s governing equations to a few POD modes.